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2011 May 07

Greyships & Spacefillers
Oblique Antstretcher

Since time immemorial, there has been a desire to find a c/5 orthogonal anteater. The motivation arises from the existence of a c/4 diagonal antstretcher, which produces a compatible oblique line of ants. By fusing the two components seamlessly, a growing spaceship could be created.

Matthias Merzenich has finally found this long-awaited anteater, enabling completion of the antstretcher.

Matthias' antstretcher, rendered in Union Flag colours to celebrate the recent Royal Wedding!

Eight copies of this can be combined to create another example of a 'space-nonfiller' (a term coined by Jason Summers), the earliest such example being discovered by him in 1999, which expanded at the vacuum speed limit.

Jason Summers' original nonfiller.

2006 May 11

Greyships & Spacefillers
2c/3 perpendicular signals through 'stripes'

extensible signal that moves at
speed 2c/3 through 'stripes' agar,
at right angles to the stripes
Hartmut Holzwart, 24 April 2006
Hartmut Holzwart and Jason Summers have been looking at signals that can propagate through an infinite medium consisting of alternating ON and OFF stripes (the same agar as in the interior of standard greyships).

It was shown in 1993 that signals travelling parallel to the striped medium must move at the speed of light -- but it turns out that non-destructive signals perpendicular to the stripes are also possible, and these follow different rules. In particular, they can move at a speed of 2c/3 orthogonally, slower than lightspeed but faster than a spaceship can travel through vacuum.

extensible symmetric 2c/3 orthogonal
signal in 'stripes' medium
Hartmut Holzwart, 9 May 2006

small symmetric 2c/3 orthogonal
signal in 'stripes' medium
Hartmut Holzwart, 9 May 2006

minimal 2c/3 stripe-crossing signal
in 'stripes' agar, based on
Hartmut Holzwart's larger original
Jason Summers, 15 Apr 2006

two short wide 2c/3 signals
Hartmut Holzwart, 2 May 2006

small 2c/3 signal in 'stripes' agar
Hartmut Holzwart, 28 Apr 2006

small symmetric 2c/3 signal
perpendicular to striped medium
Hartmut Holzwart, 26 April 2006

unfinishable spacefiller fragment with a higher growth rate
than is attainable in vacuum
Hartmut Holzwart, 26 April 2006

2006 April 03

Greyships & Spacefillers
Chicken-Wire-Agar Greyships

'chicken-wire' agar greyship with variable-width chicken-wire
Hartmut Holzwart, 30 March 2006
Hartmut Holzwart has produced some examples of an alternate type of greyship. Except for the 'Christmas tree' ships, previous greyships' stable central sections have been made up of continuous stripes of ON and OFF cells. However, central sections with stripes made up of alternate strips of ON and OFF cells (with at least two cells per strip) are also stable, and it is possible to construct greyships that can escort this kind of 'chicken-wire' agar pattern.

'chicken-wire' agar greyship with width-3 chicken-wire
Hartmut Holzwart, 30 March 2006

'chicken-wire' agar greyship with width-2 chicken-wire
Hartmut Holzwart, 30 March 2006

'chicken-wire' agar greyship with width-7 chicken-wire
Hartmut Holzwart, 30 March 2006

'chicken-wire' agar greyship with width-5 chicken-wire
Hartmut Holzwart, 30 March 2006

2006 March 24

Greyships & Spacefillers
c/4 greyships

small extensible c/4 greyship
Hartmut Holzwart, 24 March 2006
Hartmut Holzwart has been continuing his work on c/4 greyships, and has produced a number of new variants on the original.

greyship enclosing chicken-wire agar
Hartmut Holzwart, 20 Mar 2006

two related c/4 greyships
Hartmut Holzwart, 24 March 2006

new c/4 greyship variant
Hartmut Holzwart, 23 March 2006

c/4 greyship: Hartmut Holzwart, 6 March 2006

new slopes for c/4 greyships
Hartmut Holzwart, 16 March 2006

c/4 greyship variant 1
Hartmut Holzwart, 16 March 2006

c/4 greyship variant 2
Hartmut Holzwart, 16 March 2006

c/4 greyship: Hartmut Holzwart, 24 March 2006

2005 December 18

Greyships & Spacefillers
Fixed-Width and Slipping-Stripe Greyships

Here are a few more greyships and related patterns constructed recently by Hartmut Holzwart:


fixed-width 2c/4 spaceship supporting a p9 wick
Hartmut Holzwart, 15 December 2005


long and short versions of a fixed-width perpendicular greyship
Hartmut Holzwart, 13 December 2005


simpler fixed-width perpendicular greyship
Hartmut Holzwart, 13 December 2005

Continue reading "Fixed-Width and Slipping-Stripe Greyships" More

2005 December 16

Greyships & Spacefillers
New perpendicular greyships

Hartmut Holzwart has incorporated a variety of new reactions, slopes, and overall shapes into perpendicular ("against-the-grain") greyships. Here is a sampling:


perpendicular-to-the-grain greyship with new back slope
Hartmut Holzwart, 29 November 2005


new greyship component shown on right side
Hartmut Holzwart, 29 November 2005


mirror-symmetric against-the-grain greyship with new back slopes
Hartmut Holzwart, 2005-11-30

Continue reading "New perpendicular greyships" More

Greyships & Spacefillers
Hybrid greyships (perpendicular and parallel stripes)


hybrid 2c/4 greyship: Hartmut Holzwart, 16 November 2005

Another recent new idea in the greyship line is the combination of perpendicular and parallel direction of travel ("with-the-grain" and "against-the-grain" ships) into the same greyship, with various interfaces between the striped regions. These, like previous greyships, can have arbitrarily large grey regions — though it's somewhat trickier to change the size in some of these cases, since the phases of several edge and interface terminations must be synchronized.


alternate hybrid 2c/4 greyship: Hartmut Holzwart, 16 November 2005


hybrid greyship: Hartmut Holzwart, 18 November 2005

Continue reading "Hybrid greyships (perpendicular and parallel stripes)" More

2005 September 06

Greyships & Spacefillers
Greyship Update

smaller 2c/4 perpendicular greyship: Hartmut Holzwart, 14 July 2005 2c/4 perpendicular greyship: Hartmut Holzwart, 14 July 2005 Hartmut Holzwart has constructed several new 2c/4 greyships (spaceships consisting primarily of alternating lines of ON and OFF cells -- see this previous post.) Here are two versions of a 2c/4 perpendicular greyship, in which the direction of travel is perpendicular to the alternating stripes, instead of parallel to them:

Perpendicular grey ship in triangle form (-1/10,1,-1/4) Perpendicular greyship in triangle form (-1,1,1/4) It's possible to shorten an arm of one of the above ships to get a triangle, as shown at right. Some further incomplete perpendicular-greyship results can be found here. Another triangle that uses some of these connections is shown at the far right.

c/3 greyship: Hartmut Holzwart, 24 July 2005 Other greyship speeds are also possible. Here is a parallel greyship that travels at c/3 instead of c/2:

2005 July 09

Greyships & Spacefillers
c/2 and 2c/4 "greyships"

2c/4 triangle greyship 2 (back slope 1/4)  Hartmut Holzwart  1 July 2005 2c/4 triangle greyship 1 (45-90-45)  Hartmut Holzwart  1 July 2005 Hartmut Holzwart and Jason Summers have been investigating possible shapes for 2c/4 "greyships" that include an extensible striped region of half-ON, half-OFF cells. Triangles, diamonds, and other shapes are possible.

2c/4 quadrilateral greyship (back slope 5/9)  Hartmut Holzwart  1 July 2005 2c/4 diamond greyship  Hartmut Holzwart  1 July 2005 This technology can be extended to produce more complex shapes with a variety of slopes. Some components also exist for a ship traveling perpendicular to the "grain" of the stripes, instead of parallel, but currently not enough to produce a complete ship. See this blog for details.

2005 May 09

Wicks & Fuses
Extensible Wickstretchers and HALFMAX

Wickstretcher 1  Hartmut Holzwart  22 April 2005 Hartmut Holzwart and Jason Summers have successfully tamed a extended family of wickstretchers, beginning with the one at right -- a p4 wickstretcher with two central lines and a p8 tail, constructed by Holzwart on 22 April 2005.

Wickstretcher 2  Hartmut Holzwart  22 April 2005 Wickstretcher 3  Hartmut Holzwart and Karel Suhajda  22 April 2005 This was followed by several related results. To the right is an alternate form of the wickstretcher, created by Holzwart, with the right side replaced by a pure p4 tail section. On the far right is another phase of the above wickstretcher, with the tail replaced by a p6 fencepost constructed by Karel Suhajda on the same day.

smaller c/2 p80 puffer  Jason Summers  24 April 2005 Starting from a related p80 puffer ship, Jason Summers produced a new smaller p80 puffer -- 8 cells wider than the known p4 ships in Paul Tooke's collection, but about 20 cells shorter. As with the old ships, there's also an alternate, much less prolific p80 orbit -- as well as a p20 "bread-and-honey" orbit (loaves are created, then converted to beehives a few generations later.)

Wickstretcher 4  Hartmut Holzwart  3 May 2005 Wickstretcher 5  Hartmut Holzwart  25 April 2005 Holzwart also produced a four-central-line wickstretcher, and later a smaller version of the original minimal wickstretcher as well (with no central lines in the wick) -- both completed by a p4 c/2 tail rather than a fencepost.

Wickstretcher 6  Hartmut Holzwart  3 May 2005 Wickstretcher 7  Hartmut Holzwart  4 May 2005 Based on a "double fencepost" pattern of Holzwart's (not shown) Summers found a way to provide an independent fencepost for each of the two active edges of a wick -- allowing any number of stable lines to be added in the middle (the example at right shows a wick with a 14-line "sandwich".) Other possible modifications include changing the phase of the two edges relative to each other, as in the asymmetrical wickstretcher and fencepost at the far right -- or simply shifting one section of the wick by two cells relative to an adjacent section, as shown by the "spacers" (four-line-thick oblongs) toward the center of the pattern below.

Half-plane-filler (HALFMAX)  Jason Summers  4 May 2005
Finally, Summers succeeded in using the new wick and fencepost technology to produce this semi-spacefilling pattern, which expands in three directions at half the speed of light -- producing a triangular region that grows to fill half the plane. [Previous spacefillers have all been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.]

Update: 9 May 2005 07:22

HALFMAX2  6 May 2005 minimal wickstretcher  6 May 2005 On May 6, Hartmut Holzwart produced smaller versions of both the original basic wickstretcher and of Jason Summers' HALFMAX pattern (far right).

Update: 26 May 2005 06:45

3-line wickstretcher  Jason Summers  21 May 2005 smaller 4-line wickstretcher  Jason Summers  21 May 2005 On May 21, Jason Summers produced sample patterns that allow the construction of wickstretchers with any number of central lines, by adding the appropriate number of four-line "spacers" to one of the four extensible base patterns. He observed: "For each number of lines, there are eight possible wicks, made by changing the relative position and phase of the two sides of the wick (except for zero lines, where there are only two)."

HALFMAX3  Jason Summers  15 May 2005 5-line wickstretcher  Jason Summers  21 May 2005 Wickstretchers with 3, 4, and 5 central lines are shown here. On the far right is Summers' latest HALFMAX optimization, backed up by one generation to reduce the population to 903 cells.